The Observability Concept in a Class of Hybrid Control systems

TL;DR

This paper explores the observability of discrete event system models derived from hybrid control systems, analyzing how continuous plant properties influence observability and presenting an observable abstraction of a double integrator.

Contribution

It introduces a detailed analysis of the relationship between continuous plant properties and DES-plant observability, and provides an observable abstraction of a double integrator.

Findings

Established the link between cellular space properties and DES-plant observability.

Analyzed the plant-symbols generation mechanism's impact on observability.

Presented an observable discrete event abstraction of a continuous double integrator.

Abstract

In the discrete modeling approach for hybrid control systems, the continuous plant is reduced to a discrete event approximation, called the DES-plant, that is governed by a discrete event system, representing the controller. The observability of the DES-plant model is crucial for the synthesis of the controller and for the proper closed loop evolution of the hybrid control system. Based on a version of the framework for hybrid control systems proposed by Antsaklis, the paper analysis the relation between the properties of the cellular space of the continuous plant and a mechanism of plant-symbols generation, on one side, and the observability of the DES-plant automaton on the other side. Finally an observable discrete event abstraction of the continuous double integrator is presented.